Punctual Structures and Primitive Recursive Reducibility
ISKANDER SH. KALIMULLIN · Lobachevskii Journal of Mathematics · 2022
Abstract In the paper we study punctual presentations of algebraic structures relative to arbitrary functional oracles. This is formalized via the notion of primitive recursive reducibility of functions and sets on the integers. We indroduce the notion of punctual families of sets relative to an oracle and propose a coding from the families into the structures preserving their punctual properties. Using this coding we find an algebraic structure which has no punctual presentations but which has a punctual presentation relative to arbitrary non-trivial oracle.